|2| = (x² + y²)'/2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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only c.d part
Transcribed Image Text:1. If z = x + iy is a complex number with x, y E R, we define
|2| = (a² + y²)!/2
and call this quantity the modulus or absolute value of z.
(a) What is the geometric interpretation of |2|?
(b) Show that if |z| = 0, then z = 0.
(c) Show that if A e R, then |Az| = |A||2|, where |A| denotes the standard
absolute value of a real number.
(d) If z1 and z2 are two complex numbers, prove that
|212| = |21||2|
and
|21 + z2| < |21| + |22|.
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